bstar_n: Computes explicitly known values of the estimates in the two...

In OrdMonReg: Compute least squares estimates of one bounded or two ordered isotonic regression curves

Description

These functions compute the values a_1^* and b_n^*, the value of the estimate of the upper function at x_1 and the value of the lower estimated function at x_n in the two ordered antitonic regression functions problem. These values can be computed via explicit formulas, unlike the values at x \in {x_2, …, x_{n-1}}, which are received via a projected subgradient algorithm. However, b_n^* enters this algorithm as an auxiliary quantity.

Usage

astar_1(g1, w1, g2, w2)
bstar_n(g1, w1, g2, w2)

Arguments

g1	Vector in R^n, measurements of upper function.
w1	Vector in R^n, weights for upper function.
g2	Vector in R^n, measurements of lower function.
w2	Vector in R^n, weights for lower function.

Value

Values of a_1^* and b_n^* are returned.

Author(s)

Fadoua Balabdaoui [e-mail]
http://www.ceremade.dauphine.fr/~fadoua

Kaspar Rufibach (maintainer) [e-mail]
http://www.kasparrufibach.ch

Filippo Santambrogio [e-mail]
http://www.math.u-psud.fr/~santambr/

References

Balabdaoui, F., Rufibach, K., Santambrogio, F. (2009). Least squares estimation of two ordered monotone regression curves. Preprint.

See Also

This function is used by BoundedAntiMeanTwo.

OrdMonReg documentation built on May 2, 2019, 1:45 p.m.